Maxwell equations for bi-isotropic media and electromagnetic energy with complex octonions

In this study, the real and complex types of the octonions, which are one of the higher dimensional number systems, are given in detailed form. The different applied field that belongs to electromagnetism, which is the important subfield of physics, has been studied by using complex octonion algebra. First of all, the different form of Maxwell equations for bi-isotrop chiral media are defined, and then by describing the octonionic Drude-Born-Fedorov constitutive equations firstly, a new octonionic field equation has been given. As the result of all calculations, the complex octonionic source equation, which contains Maxwell equations, has been obtained as the compact, useful, easy and elegant manner. Finally, it is pointed that there is a similarity between the isotrop and bi-isotrop media for this octonionic source equation. Later, by means of Maxwell equations that have no charge and current densities, it is made that the complex octonionic representation of the Poynting theorem, which is about to energy conservation in electromagnetism, has been operated. It is seen that this result is compatible with the result of classical electromagnetism.